CHC Theory, Research Link

Fluctuations in attention are related to fluid but not crystallized intelligence

Attentional Control and Fluid Intelligence

There are many defensible ways to slice the ability domain. In a previous post, I put fluid intelligence, working memory capacity, and processing speed together in a conceptual grouping called Controlled Attention. I did not do this capriciously but on my review of the available evidence. However, the precise nature of the ways in which these abilities depend on attentional control is still being explored.

In what I consider to be an important paper, Unsworth and McMillan (2014) provide direct evidence that fluid intelligence test performance is related to moment-to-moment fluctuations of one’s attentional state. The paper consists of three experiments designed to tease apart various explanations of the positive correlation between test item performance and self-rated attentional state measured before each item (ranging from 1 = not at all focused on the task to 10 = totally focused on the present task).

Overall findings

  1. Test performance was not negatively affected by having to complete attentional state ratings.
  2. Self-rated attentional state predicted performance on fluid intelligence test items but not on crystallized test items.
  3. Participants with the most variability in self-rated attentional state from item to item performed more poorly on fluid intelligence test items than did people with more stable levels of self-rated attentional state. Thus, attentional control, in accordance with theory, appears to be an important component of fluid intelligence.

One of my suspicions was that is that participants might justify poor perceived performance on a previous item by claiming low levels of attention before the next item. It might be easier on one’s self esteem to claim, “That last item was hard because I am feeling scattered, not because I am not smart.” However, this explanation is undermined by the fact that self-rated attentional state predicted performance on fluid intelligence test items whether the items were in ascending level of difficulty or in random order. Even so, it would have been nice to have seen analyses showing that attentional state predicted performance on the next item more strongly than it “predicts” performance on the previous item.

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CHC Theory

Fluid and Crystallized Intelligence in the Classroom and on the Job

Fluid intelligence is the ability to solve unfamiliar problems using logical reasoning. It requires the effortful control of attention to understand what the problem is and to work toward a logically sound answer. People with high fluid intelligence are able to figure out solutions to problems with very little instruction. Once they have found a good solution to a problem, they are able to see how it might apply to other similar problems. People with low fluid intelligence typically need hands-on, structured instruction to solve unfamiliar problems. Once they have mastered a certain skill or solution to a problem, they may have trouble seeing how it might apply in other situations. That is, their newfound knowledge does not generalize easily to other situations.

— Schneider & McGrew (2013, p. 772)

Gf in the Classroom and on the Job

Crystallized intelligence is acquired knowledge. When people solve important problems for the first time, they typically remember how they did it. The second time the problem is encountered, the solution is retrieved from memory rather than recreated anew using fluid intelligence. However, much of what constitutes crystallized intelligence is not the memory of solutions we personally have generated but the acquisition of the cumulative wisdom of those who have gone before us. That is, we are the intellectual heirs of all of the savants and geniuses throughout history. What they achieved with fluid intelligence adds to our crystallized intelligence. This is why even an average engineer can design machines that would have astounded Galileo, or even Newton. It is why ordinary high school students can use algebra to solve problems that baffled the great Greek mathematicians (who, for lack of a place-holding zero, could multiply large numbers only very clumsily).

Crystallized intelligence, broadly speaking, consists of one’s understanding of the richness and complexity of one’s native language and the general knowledge that members of one’s culture consider important. Of all the broad abilities, crystallized intelligence is by far the best single predictor of academic and occupational success. A person with a rich vocabulary can communicate more clearly and precisely than a person with an impoverished vocabulary. A person with a nuanced understanding of language can understand and communicate complex and subtle ideas better than a person with only a rudimentary grasp of language. Each bit of knowledge can be considered a tool for solving new problems. Each fact learned enriches the interconnected network of associations in a person’s memory. Even seemingly useless knowledge often has hidden virtues. For example, few adults know who Gaius and Tiberius Gracchus were (Don’t feel bad if you do not!). However, people who know the story of how they tried and failed to reform the Roman Republic are probably able to understand local and national politics far better than equally bright people who do not. It is not the case that ignorance of the Gracchi brothers dooms anyone to folly. It is the case that a well-articulated story from history can serve as a template for understanding similar events in the present.

— Schneider & McGrew (2013, pp. 772–773)

Gc in the Classroom and on the Job
Gf Gc Typology

The pictures are previously unpublished (and not to be taken too seriously).

Definitions from:

Schneider, W. J. & McGrew, K. S. (2013). Cognitive performance models: Individual differences in the ability to process information. In S. Ortiz & D. Flanagan (Sec. Eds.), Section 9: Assessment Theory, in B. Irby, G. Brown, & R. Laro-Alecio & S. Jackson (Vol Eds.), Handbook of educational theories (pp. 767–782). Charlotte, NC: Information Age Publishing.

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

Fluid Intelligence, Defined

Mentioning fluid intelligence at cocktail parties as if it were a perfectly ordinary topic of conversation carries with it a certain kind of cachet that is hard to describe unless you have experienced it for yourself. Part of Gf’s mystique can be attributed to Cattell’s (1987) assertions that Gf is linked to rather grand concepts such as innate ability, genetic potential, biological intelligence, mass action, and the overall integrity of the whole brain.[1] Heady stuff indeed!

At the measurement level, Gf tests require reasoning with abstract symbols such as figures and numbers.[2] Good measures of Gf are novel problems that require mental effort and controlled attention to solve. If a child can solve the problem without much thought, the child is probably making use of prior experience. Thus, even though a test is considered a measure of fluid intelligence, it does not measure fluid intelligence to the same degree for all children. Some children have been exposed to matrix tasks and number series in school or in games. Fluid intelligence is about novel problem solving and, as Kaufman (1994, p. 31) noted, wryly pointing out the obvious, a test is only novel once. The second time a child takes the same fluid intelligence test, performance typically improves (by about 5 points or 1/3 standard deviations, Kaufman & Lichtenburger, 2006). This is why reports that fluid intelligence can be improved with training (Jaeggi, Buschkuehl, Jonides, & Perrig, 2008) cannot be taken at face value.[3] Just because performance has improved on “Gf tests” because of training does not mean that Gf is the ability that has improved.

At the core of Gf is the narrow ability of Induction. Inductive reasoning is the ability to figure out an abstract rule from a limited set of data. In a sense, inductive reasoning represents a person’s capacity to acquire new knowledge without explicit instruction. Inductive reasoning allows a person to profit from experience. That is, information and experiences are abstracted so that they can be generalized to similar situations. Deductive reasoning is the ability to apply a rule in a logically valid manner to generate a novel solution. In CHC Theory, deductive reasoning is called General Sequential Reasoning. Although logicians have exquisitely nuanced vocabularies for talking about the various sub-categories of inductive and deductive reasoning, it will suffice to say that everyday problem solving typically requires a complex mix of the two.

Inductive and deductive reasoning can be found in multiple places in CHC Theory. Whenever inductive and deductive reasoning are applied to quantitative content, they are called quantitative reasoning. For mysterious reasons, inductive and deductive reasoning with quantitative stimuli tend to cluster together in factor analyses. Inductive and deductive reasoning also make an appearance in Gc. Whenever inductive and deductive reasoning tasks rely primarily on past experience and previous knowledge, they are classified as measures of crystallized intelligence. Many researchers have supposed that the Similarities subtest on Wechsler tests contains an element of fluid reasoning because inductive reasoning is used to figure out how two things or concepts are alike. If the question is something like, “How are a dog and a cat alike?” then it is very unlikely that a child arrives at the correct answer by reasoning things out for the first time. Instead, the child makes an association immediately based on prior knowledge.

Researchers are not satisfied with accepting Gf as a given. They wish to know the origins of Gf and to understand why some people are so much more adept at abstract reasoning than other people are (Conway, Cowan, Bunting, Therriault, & Minkoff, 2002). One hypothesis that is still being explored is that fluid reasoning has a special relationship with working memory. Working memory is the ability to hold information in mind while using controlled attention to transform it in some way (e.g., rearranging the order of things or applying a computational algorithm). Many researchers have noted that tests of fluid reasoning, particularly matrix tasks (e.g., WISC-IV Matrix Reasoning), can be made more difficult by increasing the working memory load required to solve the problem. Kyllonen and Christal (1990) published the provocative finding that individual differences in Gf could be explained entirely by individual differences in working memory. Many studies have attempted to replicate these finding but have failed. Most studies find that Gf and working memory are strongly correlated (about 0.6) but are far from identical (Kane, Hambrick, Tuholski, Wilhelm, Payne, & Engle, 2004).

Just as we have distinguished between statistical g and theoretical g, it is important to note that there is a difference between the Gf that is measured by Gf tests and the Gf that is written about by theorists. Some of Cattell’s hypotheses about Gf have stood the test of time, whereas others have not held up very well. For example, the heritability of Gf is not higher than that of Gc, as Cattell’s theory predicts. I mention this because it is probably not justified to claim that because a child scores well on Gf tests, the child has high innate talent or that the child’s biological intelligence is high.

Most of the effects of Gf on academic achievement are mediated by Gc (i.e., better reasoning leads to more knowledge which leads to higher achievement). However, Gf seems to have a special relationship with complex problem solving in mathematics. Because Gf tests measure abstract reasoning, it is unsurprising that they would predict performance in an abstract domain such as mathematics (Floyd, Evans, & McGrew, 2003).


[1] Horn (1985) tended to de-emphasize the biological/genetic interpretation of fluid intelligence.

[2] Test developers have tried to create Gf measures with verbal content (e.g., WJ-R Verbal Analogies or SB5 Verbal Fluid Reasoning) but find that verbal Gf tests do not always load on the same factor as traditional Gf tests (Canivez, 2008; Woodcock, 1990). It is possible that the KAIT Logical Steps subtest may be the only commercially available verbal Gf test that does not have substantial loadings on Gc (Flanagan & McGrew, 1998; Immekus & Miller, 2010), possibly because it does not use the verbal analogy format.

[3] See Moody (2009) for a discussion of other methodological problems that may have compromised the validity of the Jaeggi et al (2008) study.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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CHC Theory, Cognitive Assessment, Research Link

Spatial memory and fluid intelligence: A small question answered very well

Siedlecki and Salthouse (2013) have conducted the kind of intelligence research I love to read. In “Using contextual analysis to investigate the nature of spatial memory,” they describe how they had noticed an incidental finding from a previous study that intrigued them and then carefully designed a battery of tests to see if the phenomenon would replicate and withstand several challenges to the original interpretation. It did.

The specific finding is that after accounting for fluid intelligence, spatial memory has no unique relationship with reference markers of verbal memory. This finding is important because it suggests that although it is fine to talk about “memory” as a conceptual category, there may not be an ability called general memory.

The evidence from this paper (and earlier studies) suggests that CHC Theory may need to be amended such that spatial memory and visual memory are distinguished. Furthermore, spatial memory seems to have a special relationship with fluid intelligence, even when fluid intelligence is measured with non-spatial tests.

What l like about this study is that its methodological rigor makes the finding much more persuasive than is the case in most individual differences research. Most studies in this area are from convenience samples and rarely are designed to test highly specific hypotheses.

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